Electronic conductance in mesoscopic systems: Multichannel quantum scattering calculations

Multichannel quantum scattering theory is employed to calculate the nonlinear two-port conductance and magnetoconductance of mesoscopic systems such as quantum well heterostructures, quantum dots and semiconductor or metallic microstructures. We employ a specially designed stable invariant embedding technique for calculating reflection and transmission amplitudes for these types of structure using a quantum rearrangement scattering formulation. The method can be applied to calculate electronic transport in many types of system in the low-temperature regime where phonon scattering is not significant. The basis set used for the degrees of freedom orthogonal to the current flow can be adiabatic (i.e. dependent on the coordinate along the current flow) or diabatic (not dependent on the coordinate). The dangers inherent in transforming an adiabatic formulation to a diabatic formulation with a limited basis set size are forcefully illustrated. The method naturally includes closed-channel effects and can incorporate complex potentials (to stimulate decay). Examples are presented, wherein we calculate the conductance and magnetoconductance as a function of system geometry, electronic potential and potential drop across two-dimensional quantum well heterostructures, and the results are explained in simple physical terms. The resonance features in the nonlinear conductance as functions of magnetic field and of orifice width in heterostructure devices are described and elucidated.